First, vorticial and/or shear flows may lead to large domain
deformations, i.e., severe mesh deformations, also with the occurence
of non-planar mesh faces, in the Lagrangian and Arbitrary
Lagrangian-Eulerian (ALE) numerical
frameworks [1]}, [2]}.
Such mesh deformations are treated by remeshing the computational
domain; then, by remapping the unknowns to the new
mesh [3]}.
An optimal remap algorithm should be accurate, cheap, and
feature-preserving, i.e., it should preserve the divergence-free
constraints, the solution positivity, and conserve mass, momentum, and
energy, cf. [4]}.
However, current remap algorithms can be too expensive, prone to
significant accuracy losses, and not feature-preserving.
Therefore, we infer that a good approximation method should be
accurate and stable even in presence of severe mesh deformations in
order to reduce the number of remeshing steps in a numerical
simulation.
